Mathematical Problem Solving

Recalculating the math curriculum at Peddie

Arjun Bhungalia ’20 and Angela Silvi ’20 step up to the front of the classroom, dry erase markers in hand. Teacher Emily Scott has just asked them to present a problem from the previous day’s homework. Bhungalia and Silvi write a series of numbers and graphs on the board and Scott monitors the ensuing discussion. Students are exploring ideas, debating theories and sharing feedback … they are working together to find a solution.

Welcome to Mathematical Problem Solving at Peddie, where students take the lead in their learning. After more than a year of research and planning, the Peddie math department replaced its traditional Geometry/Algebra II sequence with Mathematical Problem Solving (MPS) I and II. The courses blend topics from algebra and geometry and strongly emphasize collaboration and analytical thinking. 

The two-course update to the math curriculum is a departure from more traditional approaches to classroom learning. There are no textbooks for this class. Instructors assign problem sets for homework and encourage students to work in study groups. Teachers do not expect students to solve every problem, but they do require them to document their thinking, and come to class prepared for an active classroom discussion.

Motivation for change

Math Department Chair Tim Corica and Associate Head of School Catherine Rodrigue formed a curriculum study group in 2015 to address department concerns, including changing skill levels of incoming students, and a lack of algebra retention for students beginning Algebra II after a year of geometry.

“More and more students arrive at Peddie having already completed a course in geometry, but they do not necessarily have a strong grasp of concepts. MPS integrates geometry earlier in the curriculum,” said Corica.

He added, “MPS also allows for continuous work with algebraic concepts throughout two years, without the interruption in algebra study created by the placement of Geometry between Algebra I and II.”

According to department faculty, MPS’s focus on problem solving has real-world applications not present in conventional models of learning.

Math teacher Andrew Caglieris, who chaired the initial curriculum study group, said that it was important to the group that problem-based learning be the focus of new courses. “The emphasis on problem solving gives students greater ownership of the learning process. It also creates an ideal environment to foster communication, collaboration, and critical and creative thinking, skills that go beyond mathematical content but are essential to succeed in today’s workplace.”

Scott echoed this sentiment. “With problem-based learning, students are developing the skills to work cooperatively with their peers. They are also learning how to discover, present and debate mathematics.”

Change, the Peddie way

After months of research, the curriculum study group proposed the idea of adding Mathematical Problem Solving to the curriculum. This prompted the formation of a curriculum development team. MPS I was added to the fall 2016 schedule and MPS II will be introduced in fall 2017.

Corica said that though the department is advancing in big ways, it is also moving forward at a calculated pace.

“We want to be innovative and I think we move a lot faster than other schools in terms of innovation, but at the same time we always move at a pace that reflects the best interests of our students,” he said.

So far, feedback from students has been overwhelmingly positive.

When surveyed last December, many MPS I students used the word “collaboration” to describe what they enjoyed most about the course. “Based on the feedback that we’ve received, we know that students in MPS are recognizing the importance of collaboration, and that’s a key component of problem-based learning,” said Corica. “And, collaboration was baked into the course as groups of teachers themselves collaborated to propose, plan, design and implement MPS,” he said.

Changes to the math curriculum have also affected the teaching style of department faculty.

“I hold myself back from saying, ‘let me show you how to do this,’” said Scott. “Instead, I give my students ample time to reason and work through the problems before I share the answer.”

Caglieris added, “MPS has reinforced my belief that what we teach needs to be presented in a meaningful context, where students are given the opportunity to discover results for themselves, giving them greater ownership of both the learning process and the concepts.”

Corica estimates that by fall 2017, approximately 220 students will be enrolled in either MPS I or MPS II. 

“That’s a big deal for us,” he said. “Eventually, we think this style of teaching will touch virtually every student at Peddie.”